%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU932^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:58 AM UTC 2026
% Result : Theorem 0.08s 0.16s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 66 ( 51 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 127 ( 13 ~; 5 |; 19 &; 80 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 61 ( 20 ^; 20 !; 21 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_2,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_3,type,
sK0: $i > $i ).
thf(func_def_4,type,
sK1: $i > $i ).
thf(f1,conjecture,
! [X0: $i > $i] :
( ? [X1: $i > $i] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= X2 )
& ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X3 = X2 ) ) )
& ( ( ^ [X2: $i] : ( X1 @ ( X0 @ X2 ) ) )
= ( ^ [X2: $i] : ( X0 @ ( X1 @ X2 ) ) ) ) )
=> ? [X4: $i] :
( ( X0 @ X4 )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM141_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $i] :
( ? [X1: $i > $i] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= X2 )
& ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X3 = X2 ) ) )
& ( ( ^ [X2: $i] : ( X1 @ ( X0 @ X2 ) ) )
= ( ^ [X2: $i] : ( X0 @ ( X1 @ X2 ) ) ) ) )
=> ? [X4: $i] :
( ( X0 @ X4 )
= X4 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i > $i] :
( ? [X1: $i > $i] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= X2 )
& ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X3 = X2 ) ) )
& ( ( ^ [X4: $i] : ( X1 @ ( X0 @ X4 ) ) )
= ( ^ [X5: $i] : ( X0 @ ( X1 @ X5 ) ) ) ) )
=> ? [X6: $i] :
( ( X0 @ X6 )
= X6 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i > $i] :
( ? [X1: $i > $i] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= X2 )
& ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X2 = X3 ) ) )
& ( ( ^ [Y0: $i] : ( X0 @ ( X1 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( X1 @ ( X0 @ Y0 ) ) ) ) )
=> ? [X6: $i] :
( ( X0 @ X6 )
= X6 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: $i > $i] :
( ? [X1: $i > $i] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= X2 )
& ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X2 = X3 ) ) )
& ( ( ^ [Y0: $i] : ( X0 @ ( X1 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( X1 @ ( X0 @ Y0 ) ) ) ) )
=> ? [X4: $i] :
( ( X0 @ X4 )
= X4 ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: $i > $i] :
( ! [X4: $i] :
( ( X0 @ X4 )
!= X4 )
& ? [X1: $i > $i] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= X2 )
& ! [X3: $i] :
( ( X2 = X3 )
| ( ( X1 @ X3 )
!= X3 ) ) )
& ( ( ^ [Y0: $i] : ( X0 @ ( X1 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( X1 @ ( X0 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: $i > $i] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= X1 )
& ? [X2: $i > $i] :
( ? [X3: $i] :
( ( ( X2 @ X3 )
= X3 )
& ! [X4: $i] :
( ( X3 = X4 )
| ( ( X2 @ X4 )
!= X4 ) ) )
& ( ( ^ [Y0: $i] : ( X0 @ ( X2 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( X2 @ ( X0 @ Y0 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X1: $i] :
( ( sK0 @ X1 )
!= X1 )
& ( sK2
= ( sK1 @ sK2 ) )
& ! [X4: $i] :
( ( sK2 = X4 )
| ( ( sK1 @ X4 )
!= X4 ) )
& ( ( ^ [Y0: $i] : ( sK1 @ ( sK0 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( sK0 @ ( sK1 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X2,sK1),skolemize(X3,sK2)],[f7]) ).
thf(f9,plain,
( ( ^ [Y0: $i] : ( sK1 @ ( sK0 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( sK0 @ ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X4: $i] :
( ( ( sK1 @ X4 )
!= X4 )
| ( sK2 = X4 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( sK2
= ( sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X1: $i] :
( ( sK0 @ X1 )
!= X1 ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( sK0 @ ( sK1 @ Y0 ) )
@ X1 )
= ( ^ [Y0: $i] : ( sK1 @ ( sK0 @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[],[f9]) ).
thf(f14,plain,
! [X1: $i] :
( ( sK1 @ ( sK0 @ X1 ) )
= ( sK0 @ ( sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
( ( sK0 @ sK2 )
= ( sK1 @ ( sK0 @ sK2 ) ) ),
inference(constrained_superposition,[],[f14,f11]) ).
thf(f18,plain,
( ( ( sK0 @ sK2 )
= sK2 )
| ( ( sK0 @ sK2 )
!= ( sK0 @ sK2 ) ) ),
inference(constrained_superposition,[],[f10,f15]) ).
thf(f19,plain,
( ( sK0 @ sK2 )
= sK2 ),
inference(trivial_inequality_removal,[],[f18]) ).
thf(f20,plain,
$false,
inference(forward_subsumption_resolution,[],[f19,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU932^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:46:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.12 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % (204936)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.16 % (204958)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.16 % (204958)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.08/0.16 % (204958)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3047312620:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.16 % (204952)lrs+10_16_si=on:nwc=1.5:random_seed=1134971198:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.16 % (204955)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2279003783:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.08/0.16 % (204954)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2398462150:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.16 % (204957)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=658123615:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.16 % (204956)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2352413129:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.16 % (204952) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-204936-204952"...
% 0.08/0.16 % (204954) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-204936-204954"...
% 0.08/0.16 % (204957) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-204936-204957"...
% 0.08/0.16 % (204956) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-204936-204956"...
% 0.08/0.16 % (204955) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-204936-204955"...
% 0.08/0.16 % (204951)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=732595703:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.16 % (204957)...printing done.
% 0.08/0.16 % (204952)...printing done.
% 0.08/0.16 % (204954)...printing done.
% 0.08/0.16 % (204956)...printing done.
% 0.08/0.16 % (204955)...printing done.
% 0.08/0.16 % (204952)Refutation found. Thanks to Tanya!
% 0.08/0.16 % SZS status Theorem for theBenchmark
% 0.08/0.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.16 % (204952)------------------------------
% 0.08/0.16 % (204952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.16 % (204952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.16 % (204952)CaDiCaL version: 2.1.3
% 0.08/0.16 % (204952)Termination reason: Refutation
% 0.08/0.16 % (204952)Time elapsed: 0.001 s
% 0.08/0.16 % (204952)Peak memory usage: 12 MB
% 0.08/0.16 % (204952)Instructions burned: 2 (million)
% 0.08/0.16 % (204936)Success in time 0.025 s
% 0.08/0.16 % Vampire exiting
%------------------------------------------------------------------------------